pinehilljoe
Staff Sergeant
Any recommendations for a good book on the Enigma? or general codes of WW II?
Looking for a book on the Enigma and other machines (2 Viewers)
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Thumpalumpacus
Colonel
Enigma will not return the same substitutes in any given human lifetime. "HH" will never in our experience return as the same two letters if they are transmitted through an Engima.
For those interested, here's an Enigma emulator: Enigma Machine Emulator - 101 Computing
For those interested, here's an Enigma emulator: Enigma Machine Emulator - 101 Computing
Yes, that is one of the weaknesses in the encryption.
Thumpalumpacus
Colonel
"Weakness"? It's a strength, in that you cannot get a crib into the code by hints like letter-frequency/word-placement/grammar and so on. If the letter "E" shows up as "W" every time, that will be an in.
The more irregular you make a code, the more secure is that code.
yosimitesam
Senior Airman
Actually it was a weakness. Because no letter encrypted to itself, this made "cribbing" easier, especially in the "header" part of an encrypted message. This and the highly formal way the Germans used the "header" or preamble in messages meant that you can align a plaintext crib easier. Simply shift the plaintext crib left to right in the first part of the message and note any place where the characters match. Then the crib cannot be contained in that strip of encoded characters and you keep shifting right to find the small group "possibles" where the crib can be found. This fact was used by the British to set the "diagonal board" on the bombes. Because no character encrypted into itself, this also resulted in certain "cycles" of possibilites and impossibilities in the encryping (based on mathematical group theory, first used by the Poles) and this allowed for further "tuning" of the plug-boards on the bombes.
From the Wiki page on "Enigma Bombe":
"The Enigma encryption is a self-inverse function, meaning that it substitutes letters reciprocally: if A is transformed into R, then R is transformed into A. The plugboard transformation maintained the self-inverse quality, but the plugboard wiring, unlike the rotor positions, does not change during the encryption. This regularity was exploited by Welchman's "diagonal board" enhancement to the bombe, which vastly increased its efficiency. With six plug leads in use (leaving 14 letters "unsteckered"), there were 100,391,791,500 possible ways of setting up the plugboard. An important feature of the machine from a cryptanalyst's point of view, and indeed Enigma's Achilles' heel, was that the reflector in the scrambler prevented a letter from being enciphered as itself. Any putative solution that gave, for any location, the same letter in the proposed plaintext and the ciphertext could therefore be eliminated."
The fact that you never get the character that you put in is a weakness as it's already deviating from pure randomness.
Thumpalumpacus
Colonel
That's not my point, though. I wasn't speaking about it not being possible to encrypt as itself, which is indeed a weakness.
I was pointing out that no matter which other letter it encrypts to, the odds of encrypting to that same of the other 25 letters is infinitesimally small, which complicates any solution. That being said, it can still show up twice as the same substitute letter. This is a subtle but palpable difference.
See above.
yosimitesam
Senior Airman
Actually, it is not infinitesimally small. The probability of 2 identical adjacent characters encrypting into a different set of 2 identical characters is 1/625, or 1/(25*25), on the Enigma.
Thumpalumpacus
Colonel
And how many "E"s are in the sentence that don't convert identically that will confuse the decrypt? For reference, the last sentence had seven "E"s. Now your difficulty is much larger.
Also, .0016 is pretty small when carried out over the course of the entire message ... and that's for the most common letter in both languages. .04 carried exponentially seven times means yeah, you've got a lot of clutter and a tiny chance of one repeat.
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yosimitesam
Senior Airman
I don't understand this argument. It is universely accepted that the Enigma not ever encrypting a letter into itself was a huge advtantage in the first step into cracking a daily key. Turing even worked out an optimum length of a possible plaintext crib: too short and the bombe would probably hit more than 4 false "stops"; too long and the probability of a first wheel turnover increased causing it to not get a "stop." Cribbing had to be done first before a bombe run was even contemplated, as the cribs determined the diagonal board and other settings of the machine. If the Enigma were not "crib-able" there would have been no bombes ever built. (The Poles invented the first ones, which were crude but worked.) So the fact that Enigma cyphertext was subject to cribbing is the first and foremost strategy of attack. Everything starts there.
Here's an excerpt from David Kahn's 2002 speech at the NSA:
From the Wiki article "Cryptalysis of the Enigma" is the following:
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The Ultra Secret by F W Winterbotham came out in about 1976 just after the time British time limit on secret materials expired. The author skims through a lot and he did not have a lot, if any, official documents to refer to. It was probably written based on memories, but it makes good reading. He was involved in the distribution of the intercepted messages after they had been analyzed.
It still bothers me that WW2 historians don't consider the effect those tip had on campaigns and the war in general.
It still bothers me that WW2 historians don't consider the effect those tip had on campaigns and the war in general.
Thumpalumpacus
Colonel
My point is that in that time-frame, and I think it still stands now, is that encryption and decryption is essentially an exercise in statistics, and that if one can increase the statistical difficulty of matching coding one might win the race.
The fact that the Germans could not predict the digital computer to be applied to Enigma doesn't mean that their prior calculations of difficulty were faulty. I'm not arguing that Enigma wasn't breakable; it clearly was. I am pointing out that massing odds against is a good thing when trying to make a code more difficult. The Germans in that era were stacking odds against codebreakers and did a pretty good job of it.
It's easier to understand once we see that codebreaking is largely an exercise in statistical analysis.
Ah okay, I misunderstood you there.
But having said that, interestingly, enigma is still crackable by using an index of coincidence. The idea is that you optimise each part of the settings one by one. The fun thing is that you get a slightly better index value if you guess one of the settings (a rotor, reflector or wire) right. So by focusing on a rotor, then move to the next and so on, you can speed up the process considerably.
You of course need to know what language the message is and you need a hell of a lot more calculation power than what was available in the '40ies.
Thumpalumpacus
Colonel
Sure. All codes are crackable. and any "in" is useful. The point I was making is that keeping ahead, statistically, matters. It certainly mattered in WWII in the Atlantic, when introducing another rotor set Allied efforts back. Cracked all the same, but it made more sense for the Germans to do that than say, "meh, we're cooked" and quit trying.
It's a statistical war. You should always try to lengthen the odds, is my point.
I'd say that no investigation of WW2 codes and Enigma/Ultra is complete without looking at the Posnan School of Cryptography. Sorry, I don't have any books to recommend. But I visited the school in Posnan in 2024, and they have an excellent learning experience. Played down by the British (I also visited Bletchley Park) is the contribution made by the Poles, who already decoded Enigma routinely before WW2 started.
yosimitesam
Senior Airman
The Poles were absolutely the first to recognize the weaknesses and exploit them, brilliantly. ("Nothing concentrates the mind like having a 'gun' pointed at it.") They were prescient to contact the French and British secret services, realizing that all their work would be lost in a German invasion, which was appearing inevitable. Their contributions are very much "underrated" in the history narratives in books about Enigma. The British would not even allow the Poles to work at Bletchley but assigned them lower level codes and ciphers to work on, at least to the ones that managed to reach Britain. Since they were "foreign nationals" the British didn't consider them 100% trustworthy, while at the same time an upstanding member of the British Upper-Class Old Boy Network, Kim Philby, was giving the secret to the Russians. I believe, also, that the British simply wanted all the historical credit for the Enigma cracking and, since they could keep everything secret, they more or less pulled that off. Until, that is, the 1970's - 1980's when the truth came out. Others have spoken of this attitude of MI6 and, IMO, they are correct.
No matter the institution or organization, when it devolves into a bureacracy the most precious thing preserved in the upper managment is "bureaucratic vanity". Their actual "mission" becomes secondary. If management has to make a choice between the two in a situation, their bureaucratic vainglory is usually chosen.
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Nick Beale
Airman
In fact there was and is no time limit on classified materials. Documents were normally released to the National Archives under the "30-year rule" unless "retained by department" for various reasons of security, international relations or plain old embarrassment. Even the released files could be "weeded" and many are simply destroyed if considered of no historical importance: you will see file jackets in the National Archives marked "preserve". As far as I know, no MI6 files have ever been released although wartime files of MI5 and SOE have. Winterbotham basically decided to take a chance, IIRC (check Wikipedia!) after something had been published in France.
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Nick Beale
Airman
When I visited Bletchley Park in 2019 and 2024, full credit was given to the Poles, including a replica of their "Bomba" machine:
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Yes, agree. The Polish work and brave generosity in giving their knowledge to the UK Government is recognised and displayed at Bletchley Park.
The whole story of the WW2 codebreaking is long and complex, with strong undercurrents of Spying and Covert operations. The British and Americans worked closely together
to achieve great success. However, the very tight security required to protect the vital secrecy of this WW2 work demanded strong policing, that continued for several decades.
Eng
